1. Field of the Invention
The present invention relates to a method of transmitting information where information is represented a series of binary digits (bits) each having one of two values The present invention also relates to a transmitter for generating such information for transmission, a transmission system for conveying such information, and a communications system for communicating such information between parties.
The present invention in its different aspects finds particular, but not exclusive, application to situations in which information is to be conveyed by means of an optical fibre waveguide in which spaced-apart, discrete, optical fibre amplifiers are used to compensate for losses caused during propagation along the optical fibre.
2. Related Art
For a receiver of a particular bandwidth at the end of such a communication system to be able to detect transmitted signals within a given error rate it must receive signals having a signal-to-noise (S/N) greater than some minimum value.
In an optical fibre transmission line with in-line optical fibre amplifiers, noise is generated by amplified spontaneous emission (ASE) in the amplifiers. The total noise generated by the optical transmission line therefore depends on the number of amplifiers in the line and the ASE noise generated by each amplifier.
The ASE noise is a function of the gain of amplifier which is given by EQU g=0.23L.sub.S.gamma./n dB (1)
where L.sub.5 is the system length in km; PA1 n is the total number of amplifiers, all assumed the same; and PA1 .gamma. is the system loss in dB/km. PA1 where B is the bandwidth in G/bits. PA1 where D is the dispersion.
The solution pulses propagating down the optical fibre transmission line will lose energy and be subject to intermittent amplification. In order to have propagation in which the distance average power of the pulse is equal to a single soliton power it can be shown that an Nth order soliton has to be launched into the optical transmission line where N is given by EQU N.sup.2 =log(g)/(1-1/g) (2)
The minimum average power Pmin necessary to achieve an S/N ratio sufficient to give a 10.sup.-14 bit error rate is EQU P.sub.min =10.sup.-4 Bn[exp(45L.sub.5 /n)-1]mw (3)
It can be shown that the pulse width required to generated the required Nth-order soliton pulse of the desired minimum average power P and bandwidth B is given by EQU t.sub.ASE =0.658 N.sup.2 BD/P (4)
Equation (4) puts a constraint on the maximum soliton pulse width, t, to achieve the desired S/N ratio.
Another source of noise which becomes increasingly important at higher bit rates is the Gordon-Haus effect: see J. P. Gordon and H. A. Haus, Random Walk of Coherently Amplified Solitons in Optical Fibre Transmission, Optics Lett 11 665-7 (1986).
This effect induces an error due to fluctuations in arrival times, t.sub.n, which occurs from the combined action of an ASE induced frequency fluctuation and dispersion. The mean square jitter can be expressed as ##EQU1##
where n's are photon numbers. The error rate due to this effect can be calculated.
The operating nonlinear dynamics imposes a second requirement that the soliton period be rather longer than the amplifier spacing L.sub.A, namely EQU t.sub.spacing &gt;(0.3DL.sub.1.alpha.).sup.1/2 (6)
where .alpha. is a safety factor of about 10. Once these two conditions of equations (4) and (7) are satisfied one observes essentially distortionless propagation of single pulses over arbitrarily large distances.
In FIG. 1 is shown a plot of amplifier spacing against pulse duration showing the three limiting processes (equations 4,5 and 6) for the example of a 6000 km system length. The G-H effect is the only one which depends on bit rate and this is plotted for three bit rates (10, 8 and 5 Gbit/s).
To operate a prior art soliton transmission system, t, the soliton pulse width, must be less than the G-H limit, less than t.sub.ASE and greater than t.sub.spacing.